Silicon (Si) drift step recovery diodes (DSRD) are opening switches that form the basis for nanosecond-scale high voltage (HV) pulsers. These pulsers are crucial to the operation of a dielectric wall accelerator (DWA), a compact particle accelerator design for proton beam radiation therapy. For the DWA to operate properly, the pulser must generate HV pulses with fast rise times and widths on the order of 1 ns at an operating frequency above 1 kHz. Several pulser designs are available that can optimally drive DSRDs. The purpose of this study is to investigate the capabilities of two DSRD-based pulsers in the context of the DWA and the required pulse parameters. The first pulser is based on a magnetic saturation transformer (MST) and a DRSD. The second pulser considered is a multi-module MOSFET-DSRD-based pulser. Additionally, Sentaurus TCAD simulations are used to study the influence of the Si DSRD doping profile on the output pulse shape. The MST-DSRD-based pulser is able to generate higher amplitude pulses than the MOSFET-DSRD-based pulser with a single module (9645 V and 1807 V, respectively). However, the multi-module MOSFET-DSRD-based pulser achieves the maximum pulse amplitude (10.9 kV) compared to MST-DSRD-based pulser (9645 V). The MOSFET-DSRD-based pulser also generates pulses with shorter pulse widths compared to the MST-DSRD-based pulser (minimum of 3 ns vs. minimum of 8.36 ns, respectively). With no compression stage, the MOSFET-DSRD-based pulser (with more than one module) generates pulses with consistently faster rise times (≤3.06 ns) compared to the MST-DSRD-based pulser (≤4.31 ns). With a compression stage, the rise times were comparable between the two pulsers (MOSFET-DSRD: 1.66 ns and MST-DSRD: 1.48 ns). Both pulsers are able to operate at 1 kHz and the MOSFET-DSRD-based pulser up to 10 kHz. Parasitic capacitance and coupling between modules of the MOSFET-DSRD-based pulser affect the pulse through their influence on the forward and reverse pumping duration. Simulations show that the p region of the DSRD should be larger than the n doped region. Simulations including a parasitic capacitance, modelling the electrical connections to the DSRD, reduce the pulse amplitude. Simulations of the pulsers incorporating SiC DSRDs show a reduction in the pulse amplitude and a widening of the pulse width in comparison to the Si DSRDs.